Q) State true or false for each of the following statements and justify in each case:
(i) 2 x 3 x 5 x 7 + 7 is a composite number.
(ii) 2 x 3 x 5 x 7 + 1 is a composite number.

PYQ: Q 26(b) – CBSE 2025 – Code 30 – Series 5 – Set 1

Ans:

(Note: Let’s understand that the composite number is a number which is greater than 1 and not a prime number.)

(i) Check if 2 x 3 x 5 x 7 + 7 is a composite number or not:

We can see that 7 can be taken as common from both the parts:

∴ it can be written as 7 (2 x 3 x 5 + 1) or 7 (31)

Now, we can clearly see that the number is greater than one and since given number has factors, hence it is not a prime number.

Therefore, the given number is a composite number.

(ii) Check if 2 x 3 x 5 x 7 + 1 is a composite number or not:

We can see that there is no common number, hence we solve it.

Hence, the number becomes: 210 + 1 = 211

Now, we can clearly see that the number is greater than one. But since given number doesn’t has factors, hence it is a prime number.

Therefore, the given number is not a composite number.

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